Home
Class 12
MATHS
Evaluate: int(dx)/(x^2(x^4+1)^(3/4))...

Evaluate: `int(dx)/(x^2(x^4+1)^(3/4))`

Text Solution

Verified by Experts

Let `I=int (dx)/(x^(2)(x^(4)+1)^(3//4))=int(dx)/(x^(2)*x^(3)(1+(1)/(x^(4)))^(3//4))`
Put `1+x^*(-4)=t rArr -(4)/(x^(5))dx = dt`
`therefore" "I=-(1)/(4)int(dt)/(t^(3//4))=-(1)/(4)*(t^(1//4))/(1//4)+c=-(1+(1)/(x^(4)))^(1//4)+c`
`=-((x^(4)+1)^(1//4))/(x)+c`
Promotional Banner

Similar Questions

Explore conceptually related problems

int(1)/(x^(2)(x^(4)+1)^(3//4))dx=

Evaluate int(dx)/(x^(4)(x^(3)+1)^(2))

Evaluate: int(3x)/(1+2x^4)dx

Evaluate: int(x)/((1-x^(4))^((3)/(2)))dx

int(1)/(x^(2)(x^(4)+1)^((3)/(4)))dx

int(1)/(x^(2)(x^(4)+1)^((3)/(4)))dx

Evaluate: int(1+x^4)/((1-x^4)^(3/2))dx

Evaluate : int(dx)/(4+3x^(2))

Evaluate: int(x)/(x^(4)+2x^(2)+3)dx